论文标题
在多项式时间内间隔离散傅立叶变换的幅度和相位的确切边界
Exact bounds on the amplitude and phase of the interval discrete Fourier transform in polynomial time
论文作者
论文摘要
我们阐明了为什么在离散傅立叶变换的幅度和相位计算精确边界的间隔算法可以在多项式时间内运行。我们从正式的角度解决了这个问题，以提供基础的数学基础，以这种算法为基础。我们表明，该算法规定的过程完全解决了间隔算术的依赖关系问题，从而在涉及离散傅立叶变换的各种应用中可用。例如，在分析精度较差的信号，缺少数据的信号以及自动误差传播和经过验证的计算时。
We elucidate why an interval algorithm that computes the exact bounds on the amplitude and phase of the discrete Fourier transform can run in polynomial time. We address this question from a formal perspective to provide the mathematical foundations underpinning such an algorithm. We show that the procedure set out by the algorithm fully addresses the dependency problem of interval arithmetic, making it usable in a variety of applications involving the discrete Fourier transform. For example when analysing signals with poor precision, signals with missing data, and for automatic error propagation and verified computations.
